👀 Views: 81 💬 Answers: 1 📅 Created: 2025-06-06

algorithm python graph-theory Python

I'm stuck on something that should probably be simple. I'm currently trying to implement Prim's algorithm to find the Minimum Spanning Tree (MST) of a connected, undirected graph using Python. However, I'm encountering unexpected results, particularly when dealing with edge cases like graphs with duplicate edge weights. The implementation sometimes returns an MST that does not include all vertices, which should not happen given that the graph is connected. Here's a simplified version of my code: ```python import heapq class Graph: def __init__(self, vertices): self.V = vertices # Number of vertices self.adj = {v: [] for v in range(vertices)} def add_edge(self, u, v, weight): self.adj[u].append((weight, v)) self.adj[v].append((weight, u)) # Since the graph is undirected def prim_mst(self): mst_set = set() min_heap = [(0, 0)] # Start with vertex 0, weight 0 total_cost = 0 while min_heap and len(mst_set) < self.V: weight, u = heapq.heappop(min_heap) if u in mst_set: continue mst_set.add(u) total_cost += weight for edge in self.adj[u]: if edge[1] not in mst_set: heapq.heappush(min_heap, edge) return total_cost, mst_set # Example of usage: g = Graph(5) g.add_edge(0, 1, 10) g.add_edge(0, 2, 6) g.add_edge(0, 3, 5) g.add_edge(1, 3, 15) g.add_edge(2, 3, 4) result = g.prim_mst() print(f'Total cost of MST: {result[0]}, Vertices in MST: {result[1]}') ``` In the above implementation, I'm using a priority queue to select the edge with the smallest weight. However, when I run this on my graph with multiple edges having the same weight, I notice that sometimes not all vertices are included in the MST, even though they should be. For example, using the edges I defined creates a scenario where the algorithm chooses to skip some edges that could lead to a valid MST. I've tried adding print statements to see the order of edge selection, but they don't reveal anything out of the ordinary. I'm testing with Python 3.9 and the heapq library is being used for the priority queue. Is there any specific condition or modification I need to make to handle these edge cases properly? Any suggestions or insights would be appreciated! For context: I'm using Python on Ubuntu. What's the best practice here?